Abstract

Suppose that $Y$ is a cyclic cover of projective space branched over
a hyperplane arrangement $D$, and that $U$ is the complement of the
ramification locus in $Y$. The first theorem implies that the
Beilinson-Hodge conjecture holds for $U$ if certain multiplicities of
$D$ are coprime to the degree of the cover. For instance this applies
when $D$ is reduced with normal crossings. The second theorem shows
that when $D$ has normal crossings and the degree of the cover is a
prime number, the generalized Hodge conjecture holds for any toroidal
resolution of $Y$. The last section contains some partial extensions
to more general nonabelian covers.